Computer Algebra Commands 4-47
Input: Level 3/Argument 1: The number of rows you want in the resulting matrix.
Level 2/Argument 2: The number of columns you want in the resulting matrix.
Level 1/Argument 3: A program that uses two arguments. An expression with the two
variables I, J can be used instead.
Output: The resulting matrix.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example: Build a 2 × 3 matrix with a
ij
=i+2j.
Command:
LCXM(2,3,« →I J 'I+2*J'»)
Result:
357
468
LDEC
Type: Command
Description: Solves a linear differential equation with constant coefficients, or a system of first order linear
differential equations with constant coefficients.
Access: Symbolic solve, !Îor P
SOLVER or !ÖDIFF
Input: Level 2/Argument 1: For a single equation, the function forming the right hand side of the
equation. For a system of equations, an array comprising the terms not containing the
dependent variables.
Level 1/Argument 2: For one equation, the auxiliary polynomial. For a system of equations,
the matrix of coefficients of the dependent variables.
Output: The solution.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example: Solve 2sin(x), with the auxiliary polynomial x
2
+1:
Command: LDEC(2*SIN(X),X^2+1)
Result: COS(X)*(cC0 -X)+(cC1 — -1)*SIN(X)
See also: DESOLVE
LEGENDRE
Type: Function
Description: Returns the nth degree Legendre polynomial.
Access: Arithmetic, !Þ
POLYNOMIAL LL
Input: An integer, n.
Output: The nth Legendre polynomial.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example: Find the Legendre polynomial with degree 4.
Command:
LEGENDRE(4)
Result: (35*X^4-30*X^2+3)/8
See also: HERMITE, TCHEBYCHEFF
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